Post-yield Behavior Research Articles

Post-yield mechanical properties of bovine trabecular bone – Relationships with bone volume fraction and strain rate

Bone finite element models, which are increasingly used to assess fracture risk in patients with degenerative bone diseases, require extensive experimental data to adequately model the material properties being assigned. Previous studies have demonstrated that bone elastic mechanical properties are dependent on density as well as strain rate, however, the effect these same variables on the post-yield behaviour of trabecular bone has not been thoroughly studied. For this study, bovine femoral samples were tested at several strain rates using three different tests devices: a conventional constant strain rate apparatus for low strain rates, a Drop Weight Impact Test device for the intermediate regime and a Split Hopkinson Pressure Bar System with magnesium bar and a PVCA pulse shaper for high strain rates. Ultimate and plateau stress, as well as absorbed energy were recorded. The results of this experimentation show that post-yield mechanical properties of trabecular bone are strain rate and volume fraction dependant. Two constitutive material models describing the Ultimate strength, Plateau stress and absorbed energy are proposed based on published models valid for elastic properties of trabecular bone.

The load-carrying capacity of sandwich beams in different collapse mechanisms

The load-carrying capacity of the symmetrical and asymmetrical sandwich beams, under a quasi-static central load, is investigated in this paper. Three collapse mechanisms such as face yield, core shear and indentation are considered for symmetrical sandwich beams. Core shear mechanism is taken into account for fully clamped asymmetrical sandwich beams. Continuity equations are established by simple ‘equal area’ method for the postyield behavior of the sandwich beams in face yield and core shear mechanisms at different boundary conditions. In indentation mechanism theoretical model, the effect of the local denting on the large deflection of the sandwich beam is taken into account. Then, finite element simulations are carried out to verify the validity of the proposed analysis, and a good agreement is presented. It is shown that in the core shear mechanism under fully clamped condition, no plateau phase is presented. The effect of the core thickness on the response of the symmetrical beams is discussed in detail. For asymmetry beams in core shear mechanism under fully clamped condition, the effect of the asymmetric factor (strength or thickness) for face-sheets on the load–deflection behavior of the postyield beams can be neglected, if the sum of the strength or thickness of the face sheets is constant.

Quantitative modeling of scratch behavior of amorphous polymers at elevated temperatures

The scratch resistance of polymeric materials is generally known to deteriorate with increasing temperature of testing. The present study focuses on quantitatively predicting the effect of temperature on the scratch behavior of amorphous polymers. The Arruda-Boyce viscoplastic model is utilized to account for temperature and strain rate dependent strain-softening and strain-hardening behaviors. The post-yield behavior predicted in this model is calibrated using the yield point determined by the Richeton cooperative model. The pressure dependent Drucker-Prager model with calibrated post-yield experimental data at various strain rates is chosen as the plastic constitutive relationship of the polymeric systems for FEM simulation. Furthermore, temperature and pressure dependent frictional behavior is input into an ABAQUS contact model to simulate the variation of the adhesion coefficient of friction (μa) during the ASTM standardized linearly increasing load scratch test. The FEM simulation findings show a good agreement with the experimentally determined scratch depth and scratch coefficient of friction (SCOF) measured using the scratch test. Usefulness of the present study for design of scratch resistant polymers at elevated temperatures is discussed.

An efficient two-scale 3D FE model of the bone fibril array: comparison of anisotropic elastic properties with analytical methods and micro-sample testing.

In this study, 3D finite element analyses (FEA) are conducted to quantify the orthotropic elastic properties and investigate the load transfer mechanism of bone at the sub-lamellar level. Three finite element (FE) unit cells with periodic boundary conditions are presented to model a two-scale microstructure of bone including a mineralized collagen fibril (MCF), the extrafibrillar matrix (EFM) and the resulting fibril array (FAY) under arbitrary loading. The axial and transverse elastic properties of the FAY computed by FEA are calibrated with unique experimental results on ovine micro-samples showing a coherent fibril orientation. They are then systematically compared with those calculated using analytical methods including the basic Voigt, Reuss and shear-lag models, the Mori-Tanaka scheme and the upper and lower bounds by Hashin and Shtrikman. The predicted axial strain ratios between the two-scales are discussed with respect to a recent small-angle X-ray scattering and wide-angle X-ray diffraction study. Beyond apparent elastic properties, the FE models provide stress distributions at both hierarchical levels, confirm the shear lag mechanisms within the MCF and between MCF and EFM and identify potential damage sites under arbitrary loading conditions. A comprehensive sensitivity analysis shows that mineral volume fraction in the fibril array is the dominant parameter on the axial and transverse elastic moduli, while the MCF volume fraction in FAY is the most sensitive variable for the ratio of axial versus transverse elastic modulus followed by the elastic moduli of hydroxyapatite and collagen. The FE model of the FAY developed and calibrated in the current study represents an anatomically realistic, experimentally validated and computationally efficient basis for investigating the apparent yield, post-yield and failure behaviors of lamellar bone in future research.

Post-yield performance of additive manufactured cellular lattice structures

In energy absorption applications, post-yield behaviour is important. Lattice structures, having low relative densities, are an attractive way to obtain effective material properties that differ greatly from that of the parent material. These properties can be controlled through the manipulation of the cellular geometry, a concept that has been made significantly more attainable through the use of additive manufacturing (AM). Lattice structures of various geometries were designed, additively manufactured and tested to assess their structural integrity as well as to investigate the effect of varying the cell geometry on the overall performance of the structures. Uniaxial tensile and compressive tests were carried out on bulk material AM samples made of 316L, followed by tests on the lattice structures. Finite element (FE) analysis was also carried out and the results compared to the experimental data. The FE simulations were able to accurately predict the elastic response of both structures; however, the post-yield behaviour did not closely match the experimental data due to inadequate beam contact resolution in the FE model. The FE model yield stress was also overestimated in the regular lattice due to the presence of manufacturing defects found only in the manufactured test samples. The stochastic structure, both experimentally and in the FE model, displayed a transition in the elastic stiffness from a lower to a higher stiffness in the elastic region. This is due to changing load paths within the lattice from the beams in contact with the compression platens to the rest of the structure. This phenomenon did not occur within the regular structure.

Crushable multiaxial behavior of sandwich foam cores: Pressure vessel experiments

The objective of this study was to characterize the multiaxial, elastic-plastic and hysteresis behavior of Divinycell PVC H100 foam using a novel pressure vessel experiment. Cyclic, elastic and post-yield behavior of the foam under uniaxial compression and tension, shear, biaxial compression and shear, triaxial compression, triaxial compression-tension and triaxial compression and shear were obtained in both out-of-plane and in-plane directions of the foam. In all the above-mentioned modes, the foam exhibited elastic-plastic response followed by damage and viscoelastic hysteresis. The Tsai–Wu failure criterion was found to be superior in predicting yielding under triaxial stress states among all the anisotropic yield criteria considered. Based on the experimental results, an elastic-plastic, viscoelastic damage model was developed and used to obtain transversely isotropic, plastic strain hardening behavior as well as viscoelastic and damage properties associated with post-yield hysteresis.

Post-yield Damping Ratio Estimation Studies for Masonry-Infilled Reinforced Concrete Frames

Damping ratio is an important and central parameter for the dynamic analysis of structures. The present study focuses on the estimation of the equivalent damping ratio in a post-yield region for RC frames, both with and without infills. One-story one-bay RC frames casted non-integrally with fly ash (FA) bricks and autoclaved aerated concrete (AAC) blocks infills are considered and are tested under monotonic lateral half-cycle loading. Post-yield behavior parameters, displacement ductility and maximum drift ratio, are used to estimate the equivalent damping ratio at each cycle of lateral loading, and empirical relationships are established. Secant stiffness and stiffness degradation for RC frames are also extracted to determine the contribution and effectiveness of type of infills. Free vibration tests on RC frame specimens are conducted subsequent to each cycle of monotonic lateral loading, and the damping ratio is evaluated. It is found that the equivalent damping ratio substantially increases for RC frames with the onset of damage in the post-yield region. The major advantage of the infilled RC frame is a drastic reduction in the maximum drift ratio. However, types of infill are found to yield equivalent damping ratio at par, suggesting similar energy dissipation capabilities. RC frame infilled with AAC block is recommended due to its higher initial as well as secant stiffness vis- $$\grave{a}$$ -vis FA brick-infilled RC frames and higher stiffness degradation that allows it to behave similar to RC frame without infill.

Deformation mechanisms and post-yielding behavior of additively manufactured lattice structures

This study develops an anisotropic generalization of the volumetric hardening model (VHM) to investigate the governing deformation mechanisms at the onset of yielding of additively manufactured lattice structure (AMLS) made of a nickel-based superalloy, Inconel 718 (IN718), under quasi-static loading. The discussion of deformation mechanisms relies on defining a new yield surface using a combination of experimental measurements and finite element simulations that enable the representation of three distinct behavioral features of IN718 lattice structures under mechanical loading including (1) tension-compression asymmetry of strut-level response; (2) tension-compression asymmetry of the aggregate response; and (3) hydrostatic pressure sensitivity of the strut-level response. Typically, the VHM is used to describe the aggregate response of lattice or foam materials to global loading. The VHM model could be directly applied at the strut-level; however, this would assume a one-to-one correspondence between the local and global response. Such an assumption is not justified a priori and could alter the evolution of the local deformation mechanisms and the resulting analysis of failure modes and structural degradation. Therefore, we introduce a modified VHM (or MVHM), which represents a more appropriate yield criterion. The Johnson-Cook damage criterion and damage evolution law, which is based on Hillerborg's fracture energy method, are coupled with the MVHM to investigate the damage initiation and evolution, and their influence on the global stress-strain response using finite element simulations.

Compressive behavior of steel-reinforced concrete-filled square steel tubular stub columns after exposure to elevated temperature

This paper presents the results of axial compression tests of steel-reinforced concrete-filled square steel tubular (SRCFSST) stub columns after exposure to elevated temperature. A total of 135 SRCFSST specimens are designed and tested, including 27 specimens that are unheated and 108 that are heated for different times. Each test examines the effects of concrete strength, width-to-thickness ratio of the square steel tube, section steel ratio and heating times on the strength, deformation and ductility characteristics of the specimen. Test results indicate that the section steel ratio has the greatest effect on the post-yield behavior of the SRCFSST stub columns. On the other hand, temperature has the greatest effect on the residual bearing capacity of the SRCFSST stub columns. The section steel ratio has the second greatest effect on the residual bearing capacity, followed by the concrete strength grade and the width-thickness ratio of the steel tube. Equations are proposed to predict the ultimate strength of the composite columns at room temperature and after exposure to elevated temperature. The computed values from the formulae are consistent with the experimental results.

Global ductility demands of RC frames with various post-yield stiffness ratio and ductility capacity ratio under near-field earthquakes

The directivity pulse motion in near-field earthquake affects the responses of structures. The response includes the roof drifts and interstory drifts, which is so-called the ductility demand. Although many studies have done in this topic, the effect of various post-yield stiffness ratio and ductility capacity ratio to the global ductility demands of reinforced concrete (RC) frames under near-field ground motion is not specifically investigated yet. The trend of global ductility demands of RC frames under near-field earthquake is the objective of this study. The frames are modeled with various fundamental period, behavior factor, plastic rotation capacity, post-yield stiffness ratio, and ductility capacity ratio. The study reveals that the effect of ductility capacity ratio on the global ductility demands is apparent as as the plastic rotation capacity changes. The global ductility demand is also found influenced by global post-yield stiffness ratio and behavior factor.

Optimal Plastic Analysis of Structures under Uncertain Conditions

In this study optimum plastic shakedown analysis of framed steel structures with semi-rigid connections (SRC) between beam and columns subjected to multi-parameter static loading presented. Since shakedown analysis does not provide information concerned with the accumulated residual displacements, complementary strain energy of the residual force (CSERF) considered as constrain to evaluate the post yield behavior of framed steel structures. The constraints on the CSERF are modelled using probabilistic and deterministic methods. To evaluate the maximum shakedown load-multipliers a numerical example is introduced, shakedown load-multipliers are calculated and safe loading domains of the framed steel structure are illustrated. The numerical results show that the constraints on CSERF, SRC and probabilistic given constraints can influence on the value of the shakedown load-multipliers.

Experimental and Analytical Study of High-Strength Steel RHS X-Joints under Axial Compression

The use of high-strength steels for tubular structures has been forbidden or permitted with some joint-strength reduction in most representative international standards. Six rectangular hollow section (RHS) X-joint specimens were tested under axial compression to investigate inelastic joint behavior. The key test parameters included brace-to-chord width ratio and grade of steels. All high-strength steel specimens exhibited sufficient strength compared with current European standards’ strength criteria; their strengths were even higher than the standard’s prescribed unreduced nominal strength. Significantly different postyielding behavior was observed depending upon the brace-to-chord width ratio and the grade of steels. It was also observed that the formulation of sidewall buckling strength in the current European standard tends to predict overly conservative results and requires further examination. A new design formula for RHS X-joints subjected to sidewall buckling was proposed in this paper based on a more realistic buckling shape. When the normalized plate slenderness ratio newly defined in this study is used in conjunction with the column curve c of the European standard, both accuracy and consistency of strength predictions were significantly improved compared with those of the strength formulas currently available.

Flexural behavior of reinforced concrete beams with high performance fiber reinforced cementitious composites

This article presents an experimental study on the flexural performance of reinforced concrete (RC) beams with fiber reinforced cementitious composites (FRCC) and hybrid fiber reinforced cementitious composites (HFRCC) in the hinge portion. Beam specimens with moderate confinement were used in the study and tested under monotonic loading. Seven diverse types of FRCC including hybrid composites using fibers in different profiles and in different volumes are employed in this study. Companion specimens such as cylindrical specimens and prism specimens are also used to study the physical properties of composites employed. The moment-curvature, stiffness behavior, ductility, crack pattern and modified flexural damage ratio are the main factors considered in this study to observe the efficacy of the employed hybrid composites. The experimental outputs demonstrate the improved post yield behavior with less rate of stiffness degradation and better damage tolerance capacity than conventional technique.

A numerical study on indentation properties of cortical bone tissue: influence of anisotropy.

The purpose of this study is to investigate the effect of anisotropy of cortical bone tissue on measurement of properties such as direction-dependent moduli and hardness. An advanced three-dimensional finite element model of microindentation was developed. Different modelling schemes were considered to account for anisotropy of elastic or/and plastic regimes. The elastic anisotropic behaviour was modelled employing an elasticity tensor, and Hill's criteria were used to represent the direction-dependent post-yield behaviour. The Oliver-Pharr method was used in the data analysis. A decrease in the value of the transverse elasticity modulus resulted in the increased material's indentation modulus measured in the longitudinal direction and a decreased one in the transverse direction, while they were insensitive to the anisotropy in post-elastic regime. On the other hand, an increase in plastic anisotropy led to a decrease in measured hardness for both directions, but by a larger amount in the transverse one. The size effect phenomenon was found to be also sensitive to anisotropy. The undertaken analysis suggests that the Oliver-Pharr method is a useful tool for first-order approximations in the analysis of mechanical properties of anisotropic materials similar to cortical bone, but not necessarily for the materials with low hardening reserves in the plastic regime.

Part I: The Analytical Model Predicting Post-Yield Behavior of Concrete-Encased Steel Beams Considering Various Confinement Effects by Transverse Reinforcements and Steels.

The purpose of the work was to propose analytical model considering double confinements (provided by both transverse reinforcements and a wide flange steel section), which was verified by the nonlinear finite element analysis considering concrete-damaged plasticity. The scope of the effort and the procedures to achieve the aim of this study included the identification of the concrete confinements provided by both transverse reinforcements and a wide flange steel section based on the elasto-plastic model in tension for both rebar/steel sections and elasto-buckling for rebars in compression. The influence of rebar buckling in the compression zone on flexural moment strength was also investigated with and without considering confining effects offered by steel sections. The analytical approach predicted a post-yield behavior of composite beams based on the confining effect offered by both the shear reinforcement and wide steel flange sections. However, for beams without axial loads, the compressive zones with high and partial confinements for concrete sections at the yield and maximum load limit state were limited when compressive buckling failure was not considered, preventing the confining factors from significantly influencing the flexural load resisting capacity. An accurate flexural capacity of composite beams can be obtained when rebar was modeled with buckling in the compression zone.

Behaviour of oil palm broom fibres (OPBF) reinforced concrete

Recent concerns on global environmental sustainability and climate change have favoured the use of natural fibres as alternatives to traditional reinforcing steel in concrete due to their low carbon footprint. Oil palm broom fibres (OPBF) which are the ribs of oil palm leaflets have average length, cross-sectional area, density and tensile strength of 900 mm, 1.837 mm2, 0.84 g/cm3 and 389 MPa respectively, hence making the fibres superior to steel in terms of strength-to-weight ratio. A study on the effect of OPBF on some mechanical properties of concrete mix of 1:1.5:3 of cement, sand and gravel respectively, was carried out. Short discrete OPBF of 50 mm length were incorporated in the fresh concrete mix at 0.5%, 1%, 1.5%, 2%, 3% and 4% of total aggregate volume. A total of two hundred and seventy-six (276) samples of 150 cubic, 63 cylindrical and 63 prismatic specimens were cast to assess compressive strength of OPBF-concrete at 7, 14, 28, 56 and 112 days, and flexural and split-tensile strengths at 28, 56 and 112 days. Bond strength between OPBF and concrete matrix was also investigated through pull-out tests. Flexural strength and splitting tensile strength of concrete were slightly improved for 0.5–1% OPBF inclusion at 28 days but do not show marked improvements at 112 days. Failure of hardened OPBF-concrete was characterised by more fibre-pull-outs than fibre-fracture but with an enhanced ductility of the composite at failure. The post-yield behaviour of OPBF-concrete shows enhanced energy absorption capacity of between 70 and 320% at 112 days, thereby possessing potential application in low-cost earthquake resistant housing.

Blends of tri-block copolymers and addition curing resins: Influence of block copolymer-resin compatibility on toughness and matrix properties on toughenability

In any sort of rubber toughening of thermosets, there are two principal influences on toughness: Morphology of the elastomer particulate phase and toughenability of the matrix resin. These two factors are difficult to separate experimentally. A new approach is presented which is based on large numbers of data. By analysing property-property-relationships an attempt is made to identify generalizable rules. A tri-block copolymer (PCL-PDMSi-PCL) is analysed in detail: By varying the molecular weights of the compatible and incompatible blocks in two different epoxy resins the influence of morphology on toughness is studied. Linear (Tg and rubbery plateau modulus) and non-linear (yield stress and post-yield behaviour) matrix properties are examined for a larger number of resin/curing agent combinations toughened with three different toughening agents in order to elucidate which matrix property controls toughenability. The same resin/curing agent array was used to study the influence of matrix polarity on morphology and properties for one PCL-PDMSi-PCL tri-block-copolymer.

Post-Yielding Behavior of Hinge-Supported Wall with Buckling-Restrained Braces in Base

A novel structural wall with hinge support and buckling restrained braces (BRBs) set in the base (HWBB) is studied. HWBB can be applied to precast manufacturing due to its considerable ductility and the separate loading mechanism in HWBB–frame structure. In elastic stage, BRBs play a brace role to make the hinged wall resist horizontal forces like a shear wall. BRBs dissipate seismic energy through plastic and hysteresis effects after yielding and the damage is only concentrated in BRBs. The performance of an HWBB is equivalent to a shear wall structure with excellent ductility and stable energy dissipation capacity. Numerical analysis indicates that the hinged wall body in the HWBB well controls the deformation mode of the structure, avoiding the concentration of story drifts, thereby protecting the remaining parts of the structure. It is revealed that the moments of the wall body will generate significant increments after BRBs yielding, and the Seismic Intensity Superposition Method is proposed to calculate the moments. In this method, nonlinear response of an HWBB can be regarded as the sum of the responses of two elastic corresponding structures excited with two parts of the seismic intensity, respectively. Modes and moments equations of the hinged wall with uniform distribution of stiffness and mass are derived, and calculation results coincide with that of the nonlinear time history analysis (NHA). For a more general case, the white noise scan method is proposed to solve the structure’s natural characteristics and to further calculate the response. Finally, the post-yielding moment calculation method and the process based on design response spectrum are proposed. It is proved that the moments from proposed Seismic Intensity Superposition Method can envelop most of the moments from NHA, and it is a good estimate of the response of HWBB in nonlinear stage.

Assessing and quantifying the earthquake response of reinforced concrete buckling-restrained brace frame structures

Due to the stable hysteretic behavior, buckling-restrained braces (BRB) have been increasingly adopted in reinforced concrete (RC) frame structures to develop a dual structural system. This investigation aims to quantify the seismic behavior of newly-constructed reinforced concrete BRB frames (RC-BRBFs). The force–deformation characteristic of dual RC-BRBFs is firstly presented and the yield displacement is derived using the story shear ratio resisted by BRB system. The seismic design procedure of dual systems for different BRB configurations (including single diagonal, V-type and inverted V-type), is developed using the performance-based plastic design approach by considering BRB postyield behavior, design target drift and global yield mechanism. 126 RC-BRBF structures corresponding to different story numbers, BRB configurations and story shear ratios are designed. The influence of story shear ratios on the design results is analyzed. The seismic response of structures subjected to 22 ground motions is investigated and compared in terms of yield mode, maximum interstory drift ratio, BRB maximum ductility and cumulative ductility, and residual drift ratio. The relationship between actual and design normalized story shear of BRBs is demonstrated and a fitting equation is proposed to quantify the actual story shear ratios. The analytical results of the present study can provide quantified insights to the seismic design of RC-BRBF structures.

Low-velocity impact of rectangular multilayer sandwich plates

The aim of the work is to investigate the low-velocity impact of fully clamped rectangular multilayer sandwich plates with metal foam cores struck transversely by a heavy mass. Analytical models considering interaction of bending and stretching induced by large deflections are developed for the dynamic response of multilayer sandwich plates. Numerical calculations of multilayer sandwich plates under low-velocity impact are conducted and analytical models can capture the numerical results reasonably. The cases of three typical impact locations are considered. Effects of loading location, the multilayer factor and shape of the striker on the structural response are discussed. It is demonstrated that the present analytical model can reasonably predict the low-velocity post-yield behavior of rectangular multilayer sandwich plates with metal foam core struck by a heavy mass.